Porosity of a Packed Bed, Void Ratio

Porosity or voidage of a packed bed of powder is defined as the volume of the voids within the bed (i.e. the volume occupied by air) divided by the total (overall) volume of the bed. The void volume includes the pores within the particles if they are porous. The pores in the particles can, however, be excluded from the definition, particularly if the application is in fluidized beds or flow through packed beds because the pores in the particles are in those cases not available to the flow. 

When porosity or voidage of a packed bed is quoted, therefore, it is important to state clearly the fact whether it has been measured inclusive or exclusive of open or closed pores. 

The value of the voidage is clearly much affected by the state of compaction of the powder and some powders can be compacted into a whole range of porosities just like in the case of bulk densities. The two properties are in fact related via the particle density in that, for a unit volume of the bulk powder, there must be the following mass balance  

The above equation gives the porosity (= voidage) of the powder and whether or not this includes the pores within the particles depends on the definition of particle density used in this evaluation - see section 2.4. 

There is a considerable confusion between the voidage defined above and the so-called void ratio often used in soil mechanics it is defined as 

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